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# Solutions for Chapter 11.1: Orthogonal Functions

## Full solutions for Differential Equations with Boundary-Value Problems | 7th Edition

ISBN: 9780495108368

Solutions for Chapter 11.1: Orthogonal Functions

Solutions for Chapter 11.1
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##### ISBN: 9780495108368

Differential Equations with Boundary-Value Problems was written by and is associated to the ISBN: 9780495108368. This textbook survival guide was created for the textbook: Differential Equations with Boundary-Value Problems, edition: 7. Chapter 11.1: Orthogonal Functions includes 21 full step-by-step solutions. Since 21 problems in chapter 11.1: Orthogonal Functions have been answered, more than 16981 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Key Calculus Terms and definitions covered in this textbook
• Annuity

A sequence of equal periodic payments.

• Compounded annually

See Compounded k times per year.

• Coordinate(s) of a point

The number associated with a point on a number line, or the ordered pair associated with a point in the Cartesian coordinate plane, or the ordered triple associated with a point in the Cartesian three-dimensional space

• Data

Facts collected for statistical purposes (singular form is datum)

• General form (of a line)

Ax + By + C = 0, where A and B are not both zero.

• Graph of an inequality in x and y

The set of all points in the coordinate plane corresponding to the solutions x, y of the inequality.

• Imaginary axis

See Complex plane.

• Modulus

See Absolute value of a complex number.

• Multiplication principle of probability

If A and B are independent events, then P(A and B) = P(A) # P(B). If Adepends on B, then P(A and B) = P(A|B) # P(B)

• Polar coordinate system

A coordinate system whose ordered pair is based on the directed distance from a central point (the pole) and the angle measured from a ray from the pole (the polar axis)

The measure of an angle in radians, or, for a central angle, the ratio of the length of the intercepted arc tothe radius of the circle.

• Reflection across the y-axis

x, y and (-x,y) are reflections of each other across the y-axis.

• Richter scale

A logarithmic scale used in measuring the intensity of an earthquake.

• Scientific notation

A positive number written as c x 10m, where 1 ? c < 10 and m is an integer.

• Solution of an equation or inequality

A value of the variable (or values of the variables) for which the equation or inequality is true

• Subtraction

a - b = a + (-b)

• Unbounded interval

An interval that extends to -? or ? (or both).

• Variable

A letter that represents an unspecified number.

• Vertex form for a quadratic function

ƒ(x) = a(x - h)2 + k

• Vertical line

x = a.